Significant Figures

1. Explain what significant figures are.2. Use Significant figures in measurements and calculations.3. Understand how significant figures impact precision.

Why do we need to know significant figures?We as scientists need to measure

things as we perform experiments.Instruments have different degrees of

precisionWe measure to the last known

calibration, and estimate the unknown.

Measurements in ExperimentsChapter 1

Significant Figures

Even though this ruler is marked in only centimeters and half-centimeters, if you estimate, you can use it to report measurements to a precision of a millimeter.

The Rules

Significant Figures – The Rules1. Nonzero numbers 1 – 9 are

always significant.

Examples: 1 meter 1 sig fig 92 liters 2 sig figs 34578 grams 5 sig figs

Significant Figures – The Rules2. Imbedded zeros (zeros between

nonzero numbers) are always significant.

Examples: 202 cm 3 sig figs10509 mL 5 sig figs2039 kg 4 sig figs90009 g 5 sig figs

Significant Figures – The Rules3. Leading zeros are never significant.4. Trailing zeros after a nonzero

number after the decimal are significant.

Examples:0.00000540 g 3 sig figs0.3700 mm 4 sig figs0.00101 L 3 sig figs

Significant Figures – The Rules5. Trailing zeros before the decimal

are significant only if the decimal point is specified.

Examples:100. dg 3 sig figs100 dg 1 sig fig8900 km 2 sig figs8900. km 4 sig figs

Exact NumbersAn exact number is a number that cannot

be changed. (Cannot be halved or split up)Ex. 2 atoms, 1 proton, a hundred dollar bill

We include most conversion factors as exact numbers Ex. 1m = 100 cm

When you work with exact numbers, you consider them to have infinite sig figs.

(You don’t have to worry about them!)

RECAP #1

Leading Zeros Imbedded Zero

0.00770800

Nonzero numbers Trailing Zeros

after the decimal

6 significant figures

RECAP #2

Leading Zeros Imbedded Zero

(none)

22060 Nonzero numbers

Trailing zero with no decimal

4 significant figures

Lets Practice!

56 meters

2 sig figs

Rule 1

20 grams

1 sig figRule 1, 5

303.0 mL

4 sig figsRule 1, 2,

4

200 kilograms

1 sig figRule 1, 5

207 kilometers

3 sig figsRule 1,2

0.7900 grams

4 sig figsRule 1,3,4

0.0096070 m

5 sig figsRule 1,2,3,4

102000 km

3 sig figsRule 1,2,5

1.10 x 102

hm

3 sig figs Rule 1, 4

2.2 x 1034 atoms

infinite sig figs

Rounding NumbersIf you have to round and the

number you are looking to round is less than 5, don’t round.Example:

214round to 2 s.f.Answer = 210

Rounding NumbersIf you have to round and the

number you are looking to round is 5 or greater, round up.Example:

215round to 2 s.f.Answer = 220

Adding and subtracting with significant figures.When adding or subtracting

significant figures, you round your answer to the least number of places after the decimal that are contained in your problem.

YOU ARE LOOKING AT PLACES AFTER

THE DECIMAL NOT SIGNIFICANT

FIGURES!

Example:2.00 + 4.0 = 6.0

You look for the least number of PLACES after the decimal.

2.00 = 2 places after the decimal4.0 = 1 place after the decimalYour answer can only have one place after the

decimal.

Example:

2.0 + 4 = 6

2.0 = 1 place after the decimal4 = no places after the decimalYour answer can not have any places

after the decimal.

Example:0.05560 – 0.001 = 0.0546

=0.055

0.05560 = 5 places after the decimal0.001 = 3 places after the decimalYour answer can only have 3 places

after the decimal.

Let’s Practice

17.0 – 0.4753 = 16.5247

Answer16.5

37.00 + 0.4753 + 19 =56.4753

Answer56

100.0 – 71.52 = 28.48

Answer28.5

0.075 + 11 + 9.2 = 20.275

Answer20

Multiplying and Dividing with Significant FiguresWhen multiplying or dividing with

significant figures, your answer must be rounded to the least number of significant figures in the problem.

YOU ARE LOOKING AT SIGNIFICANT FIGURES NOT

PLACES AFTER THE DECIMAL!

Example20.0 x 14.22 =

284.4

Answer284

430 x 0.003 = 1.29

Answer1

2020 x 790.00 = 1600000

Answer1.60 x 106

50.0 / 0.020 = 2500

Answer2500

50.0 / 0.02000 = 2500

Answer2.50 x 103